Transcription
Hello everybody and welcome back. Today I want to define a few key terms that we're going to be using throughout this CT Physics course. Each term will relate specifically to the geometry of third generation CT scanners, and as you'll see, each one of these concepts actually isn't that difficult to understand in isolation, but that mustn't undermine their importance as we move on to more complicated topics later on.
Now, in CT Imaging, essentially what we're doing is we're taking a three-dimensional data acquisition system, a three-dimensional X-ray beam falling onto an array of detectors, and we're converting that data into, for the most part, a two-dimensional image that we're displaying on our screen. And knowing how the three-dimensional geometry needs to be accounted for in order to accurately process that image becomes incredibly important. And understanding these terms that we're going to look at today will help us with that understanding.
Now, the first thing that I want to look at when looking at this CT beam is what's known as The Fan Angle. Now, the fan angle defines the angle of the X-ray beam that needs to extend from the anode in order for the X-ray beam to cover the entire width of the X-ray detectors on the other side of our CT machine. So this angle here is what's going to be the fan angle, and we can label it with a $\theta$ here. That fan angle in CT machines is generally between 50 and 60 degrees in third generation CT scanners, depending on the size of the field of view that we're trying to create. And we're going to look at how the fan angle becomes incredibly important when calculating the maximum possible field of view.
Now, when we look at third generation CT scanners, we describe that X-ray beam as being a fan beam. Now, that's technically not correct. It does fan out like that, but a fan beam shouldn't have any width in the Z axis of our plane, into and out of the screen here. The fan angle is the angle of the beam in the XY plane, the axial plane, cutting across the patient parallel to our screen here. In fact, third generation CT scanners do have some width in the Z axis, and this angle that's created is what's known as The Cone Angle. I'm going to represent it here with a $\theta$.
Now, in fact, the third generation X-ray beam is a cone beam. Technically, it's a narrow cone beam, and it's made narrow by these collimators that have narrowed down the beam in the Z axis. So what we're dealing with is fan beam and cone beam geometry, X-ray beam that's fanning out in the XY plane as well as the Z plane.
Now, this cone angle is going to make a beam heading out towards our detectors, and that beam has some width. We can see that the width of the beam here is covering data along the Z axis of our patient. If we think about the Cartesian plane that's created around the patient, the XY plane is going to be the axial plane where the X-rays are passing through the patient, and the Z axis is going to be the longitudinal plane as the patient moves through the CT scanner. And that cone angle has created some width in the Z axis, and that width is what's known as the beam width, the width of the beam. It makes sense now.
Notice how the beam width gets wider as we extend out towards the detectors. The beam width changes depending on the distance away from the detector. The further away from the detector in cone beam geometry, the narrower the beam is going to be.
Now, when we started with CT scanners, saying second generation CT scanners, the detector was a one single row of detectors, and the beam width that matched the row of detectors would be the same as our slice thickness. Now that we're creating more width because we've got more detectors to cover in the Z direction of our plane, beam width no longer equals slice thickness. Slice thickness is not defined by the collimator, that's what the beam width is defined by, how wide we collimate this beam. Slice thickness is determined by the width of the detectors in which we are acquiring the data. We can take each row of these detectors and create a single axial slice, a single axial image that we're going to display on our machines. So the width of the detector is going to determine the slice thickness.
Now, what we can do, we may not want just one detector with slice thickness, say 0.5 mm slice thickness. We might want slightly thicker than that because when we have a very small slice thickness, we've got very few X-rays actually incident onto that detector, and our signal to noise ratio is going to be very, very low. We'll have a lot of noise in the background. If we want more signal, we can bend those detectors together, we can group these detectors together and take the detector data from all four of these adjacent detectors and count them as one. There, we're getting more signal, our signal to noise ratio is going to be better, and we're going to look at this closely when we look at image quality later on. So it's the width of the detectors that we use to generate a single slice that's going to determine the slice thickness. It's not the beam width that we've collimated onto our detectors here, and this is a function of multi-detector CTs.
Now, this width of the slice thickness, as we've seen, can change depending on the number of detectors that we're using to create each axial slice. Incredibly important to understand that difference between beam width and slice thickness.
Now, while we're on the concept of beam width, you can see here in this image, I've generally made the width of the beam exactly the same as the detectors. Now, in practice, we actually make the beam width slightly wider than the detectors in the Z axis of our scan. That's because the focal spot is not a point source. The focal spot has some width. Whenever you collimate a beam with a focal spot that has some width, you get what's known as a penumbra, a region on the lateral parts of our beam width that have fewer X-ray photons because of the geometry of the focal spot in relation to the collimators. And I've talked about that in the X-ray physics learning pathway.
Now, making the beam width slightly wider than the detectors will mean that the X-rays incident on the detectors will have full normal intensity. They won't include the penumbra that we've created with that wider focal spot and collimators. Making the beam width slightly wider than the detectors is obviously going to increase the patient dose. We're exposing the patient to some X-rays that aren't going to contribute to our image, and it's going to ever so slightly decrease image quality because now we've created regions of scatter that can still be incident onto our patient. We've increased the width in the Z axis.
Okay, so now we've looked at the angles that determine the 3D geometry of the beam. The fan angle determines the width of that beam in the XY plane, and the cone angle determines the beam width in the Z axis. Now we're going to look at some of the geometry that is created when the third generation CT scanner rotates around the patient. This X-ray beam is moving over time, and that's going to create different geometry.
Now, what we can do is draw a line here that connects the anode directly to the detectors here, and it bisects the fan angle. It's down the middle of our beam. This is what's known as the source to detector distance. We can actually calculate this distance. We want to know this distance.
Now, when a third generation CT scanner rotates, there will be a point that is the center of that rotational axis. That point doesn't move. Generally, in a 512x512 pixel array, that point is what's known as the isocenter. It represents the pixel at 256x256 in the XY coordinates. In this example, I'm going to make the isocenter directly in the middle of the source to detector distance. It doesn't have to be in the middle, but by convention, it often is. This point here is what's known as the isocenter, and the distance from the source to the isocenter can be represented by the letter S here.
Now, importantly, the isocenter is the axis of rotation for a third generation CT scanner. It's not halfway from the source to detector distance. It often is, but it doesn't have to be.
If we were to draw a small circle around the isocenter and then expand that circle out until it hit the edge of our fan beam here, we would create what's known as our maximum field of view. The maximum field of view is the area in which we can accurately calculate attenuation data. Anything that falls outside of this maximum field of view, we're not going to be able to accurately calculate attenuation data. So our patient needs to sit within this maximum field of view.
Now, how do we go about calculating the size of this maximum field of view? How do we ensure that our patient is going to fit in the maximum field of view? We're going to place the patient directly at the isocenter first of all. We want as much of the patient to sit within this maximum field of view, and to do that, we place them here. If we were to draw a line here that was a tangent to the edge of our X-ray field here, creates a right angle here, we can then go about calculating this distance using trigonometry. We know that the fan angle here has been divided by two by the central line that we've drawn here, and we created this angle $\theta$, which is the fan angle divided by two. If we were to take the sine of this angle, we would be then calculating the opposite length over the hypotenuse length of this triangle. We could create this formula: sin($\theta$) would equal opposite over hypotenuse. Let's write it as the radius of the circle over the source to isocenter distance, which is the same as this hypotenuse side here.
Now, we will know the source to isocenter distance within our machine. Let's say it's 50 cm. We don't know the radius of our maximum field of view, but we will know the fan angle. Say the fan angle is 60 degrees. Half of the fan angle is going to be 30 degrees. We can then rearrange this formula to take the denominator on the right hand side over, and we know that the sine of $\theta$, which in this case is going to be 30 degrees, multiplied by the distance from the anode to the isocenter, is going to give us this radius here. Now, the sine of 30 is actually 0.5, and we said that our distance in this example is 50 cm. So 50 cm * 0.5 is going to tell us that the radius of our maximum field of view is 25 cm.
Now, often the maximum field of view is defined by the diameter of the maximum field of view, so we need to times the radius by two. That's going to give us the diameter. Notice how increasing the fan angle is going to increase the maximum field of view. Increasing the source to isocenter distance is also going to increase the maximum field of view. Both of those factors determine how much of the patient we can scan.
You might also notice that when you look at the X-ray beam here, the beam fans out. It's not parallel geometry like we looked at in first generation CT scanners. There's a divergence of the X-ray beam, and that makes a major difference when we look at how objects are going to cast a shadow onto our detectors. Remember, X-rays are just electromagnetic radiation, they're the same as light, just at a different frequency. So we're still casting a shadow onto the detectors. If we looked at an object like this and we were to take the X-rays that touched both flanks of that object, we would see that the shadow cast on the detectors is much larger than the object itself. That object has been magnified. Our data is representing a magnified version of what's actually happening within the patient at the level of the isocenter. And we can calculate this magnification using what's known as a magnification factor.
The magnification factor at the isocenter takes the source to detector distance, this distance here, and divides it by the source to isocenter distance here. Now, let's take an example where the isocenter here isn't exactly halfway. We have a magnification factor where the source to detector distance is 90 cm, the distance from the anode to the detectors, and the source to isocenter distance is 50 cm. It's slightly over halfway here. That means our magnification factor is going to be 1.8.
Now, why does this become important? Whenever you see figures quoted in CT Imaging, say a CT machine says to you that our slice thickness, our minimum slice thickness is going to be 0.5 mm, an extremely thin slice. The slice thickness that they're quoting is actually the slice thickness that happens at the isocenter. It's not the slice thickness or detector width at the detector level. We need to account for that using this magnification factor. So a CT machine says that the slice thickness is 0.5 mm at the isocenter, our detector width is going to be 0.9 mm. Let's make that a bit easier with mental math. If the slice thickness was 1 mm at the isocenter, it's actually going to be 1.8 mm at the detector level. A detector in this system that's 1.8 mm wide is going to give us an effective slice distance of 1 mm at the isocenter.
Now, importantly, that's at the isocenter. It changes depending on where you are within the patient, and we're going to look at that specifically again when we look at image quality. But it's important to realize because of the diverging beam, we get magnification in that beam.
The last geometric concept that I want to look at is what's known as anode heel effect. If you've done X-ray physics, you'll know that over the field of view of the X-ray beam, we get a change in X-ray intensity because of the anode angle that we've created. If we look side on here, we've got an anode angle. I want to represent that diagrammatically. Here's our anode, and we shine an X-ray beam onto that anode. X-rays are going to be produced here with Bremsstrahlung and characteristic radiation. X-rays that are heading out this part of the beam are going to travel through much more of the anode than X-rays heading out this part of the X-ray beam through the field of view here. X-rays are going to be attenuated by the tungsten anode here, and the intensity of the X-ray beam, the actual number of X-rays passing out this end of the X-ray beam, is going to be fewer than on this side of the X-ray beam. And this ranging in intensity, the ranging in number of X-rays, the fluence of the X-ray beam will change based on this anode angle. And we've seen in X-ray Imaging that changing the anode angle or changing the field of view or changing the source to detector distance, it's all going to have an effect on the anode heel effect.
In CT Imaging, it's slightly different. In X-ray Imaging, we would just put the more intense part of the beam over a denser region, say the pelvis, if we were doing an abdominal pelvic X-ray, and the less intense part over the part of the patient that's less dense, and we would try and even out the fluence or the intensity of the X-rays that hits our detector. In CT Imaging, this isn't the case. We know that this anode lies parallel to the XY plane that we are imaging, and we collimate that beam very tightly. We create a very narrow beam. This is going to represent our cone width, our beam width, and you'll see that the anode heel effect doesn't play very much effect here because we've got such a narrow beam in the Z axis. The anode heel effect doesn't happen in the XY plane. That anode angle stays the same, parallel to the beam that we are generating.
So that's about all in terms of geometry that I want to talk about in CT Imaging. Now we're going to apply that geometry and see how that influences how we go about creating that 2D image. In the next talk, we're going to be talking about acquisition types: axial scanning versus helical or spiral scanning, a concept that comes up over and over again in exams. I've actually got multiple questions about modes of acquisition in the question bank that I've linked in the description box below, so check that out if you're studying for an exam. Otherwise, I'll see you all in the next talk. Goodbye everybody.